The title is a reference to Enrico Fermi's famous question: "Where is everybody?" In its context, what he meant was: "if there are alien civilisations, why haven't we seen any evidence of them yet?" This is a book about the search for extraterrestrial intelligence written by someone who knows whereof he speaks, for he is chair of Seti's post-detection science and technology taskgroup. In other words, if everything goes according to protocol (which it probably won't, but never mind), he gets to say "hello" first to any aliens who say "hello" to us. This might seem an awesome responsibility, but Professor Davies is used to dealing with concepts that are somewhat out of the ordinary. The last book by Davies that I reviewed, The Goldilocks Enigma, was full of mind-blowing stuff, intelligibly and plausibly presented. And here is more of the same, or similar.

You could question the wisdom of trying to see if anyone else is out there. (There are people who want to stop others making deliberate attempts to contact aliens on the grounds that they may find this planet rather covetable and kick us off it. To which one can only say that they have not seen Harlesden on a wet Sunday afternoon.) You may also question the very discipline of exobiology, or imagining what alien biology is like. After all, it isn't as if anyone has anything to go on.

But that has not stopped Davies writing another superb science book, which both sticks to its remit and touches on larger issues in a manner that helps them slip down easily without making us feel that we have been condescended to. This is an intelligent, enthusiastic man who communicates his enthusiasm, and the scientific concepts that are his subject, in clear prose that you do not have to be a scientist to appreciate.

If you do not accept the sentiment behind the book's epigraph – Arthur C Clarke's remark that "sometimes I think we're alone in the universe, and sometimes I think we're not. In either case the idea is quite staggering" – then perhaps this is not for you. Which would be a pity, for Davies brings many elements into play. "Contemplating a seriously alien intelligence . . . means we must jettison as much mental baggage as possible," Davies says in his introductory chapter. He then goes on to restock our minds with such concepts as the possibility of there being different forms of life from the carbon-based kind we are so familiar with (the next best bet is not, paceStar Trek, silicon-, but arsenic-based), and which may yet be discovered on earth; the odds against life, let alone intelligent life, arising anywhere (astronomical, basically); the habitability windows of potential civilisations; the possibility of nanoprobes encoded in viruses or in our very own DNA; not to mention quantum computers, Dyson spheres (a shell surrounding a sun at planetary orbital distance), and the idea of post-biological intelligences.

On the question of computers versus the human brain, he will make you feel fairly good: a computer that can perform as many operations per second – or "flops" – as the brain is possible, but "the big difference is that the computer would consume several megawatts to do it, whereas the brain gets by on three meals a day". And who could not love the rubric describing Fig 11? "Whimsical depiction of energy extraction from a black hole."

And there are some scientists one cannot help but love: the ones who are both romantic and practical, who got fired up as children watching, say, 2001: A Space Odyssey and have devoted their lives to seeing whether there is anything in it. Davies is such a one. His conclusions are open-minded, capable of withstanding robust inquiry, albeit a little depressing. Apparently alien intelligence is overwhelmingly likely to be post-biological, a "matrioshka brain" which amuses itself by solving ever more abstruse mathematical theorems. "I confess this seems to me a rather narrow vision of thrill-seeking," Davies writes ruefully, "but it may be that an Extraterrestrial Quantum Computer would rapidly exhaust all other possible experiences." Even, it would seem, the pleasure of reading this very entertaining and mind-expanding book.

It will soon be half a century since the American astronomer Frank Drake first pointed a radio telescope at the star Tau Ceti in the hope of picking up an extraterrestrial broadcast, and we still haven't heard anything. So is there anyone out there, asks Robin McKie